Effects of substrate-ion density gradients on light-ion acceleration from ultraintense laser pulse irradiated thin-foils

A general solution of the electrostatic potential that determines the maximum light-ion energy is derived for the test-particle acceleration model by taking into account the influence of the substrate-ion density gradient. It is shown that the substrate-ion density structure is also dependent on laser pulse duration. In the picosecond or sub-picosecond regime, the decreasing density gradient of the substrate-ions leads to an evident reduction in the acceleration efficiency of the light-ions. However, this kind of influence is negligible in the ultrashort regime.